System for measuring of both circular and linear birefringence

ABSTRACT

A system and method for precisely measuring low-level linear and circular birefringence properties (retardance and direction) of optical materials ( 26 ). The system incorporates a photoelastic modulator ( 24 ) for modulating polarized light that is then directed through a sample ( 26 ). The beam (“Bi”) propagating from the sample is separated into two parts, with one part (“B1”) having a polarization direction different than the polarization direction of the other beam part (“B2”). These separate beam parts are then processed as distinct channels. Detection mechanisms ( 32, 50 ) associated with each channel detect the time varying light intensity corresponding to each of the two parts of the beam. This information is combined for calculating a precise measure of the linear and/or circular retardance induced by the sample, as well as the sample&#39;s fast axis orientation and direction of circular retardance.

TECHNICAL FIELD

[0001] This invention relates to a system for measuring both linearbirefringence and circular birefringence (magnitude and angle) in atransparent sample.

BACKGROUND AND SUMMARY OF THE INVENTION

[0002] Many important optical materials exhibit birefringence.Birefringence means that different polarizations of light travel atdifferent speeds through the material. These different polarizations aremost often considered as two components of the polarized light, onebeing orthogonal to the other.

[0003] Birefringence is an intrinsic property of many optical materials,and may also be induced by external forces or fields. Retardation orretardance represents the integrated effect of birefringence actingalong the path of a light beam traversing the sample. If the incidentlight beam is linearly polarized, two orthogonal components of thepolarized light will exit a linearly birefringent sample with a phasedifference, called the retardance. If the incident light beam iscircularly polarized, two orthogonal components of the polarized lightwill exit a circularly birefringent sample with a phase difference,called the retardance. The fundamental unit of retardance is length,such as nanometers (nm). It is frequently convenient to expressretardance in units of phase angle (waves, radians, or degrees), whichis proportional to the retardance (nm) divided by the wavelength of thelight (nm). An “average” birefringence for a sample is sometimescomputed by dividing the measured retardation magnitude by the thicknessof the sample.

[0004] The need for precise measurement of birefringence properties hasbecome increasingly important in a number of technical applications. Forinstance, it is important to specify and control the residual linearbirefringence (hence, the attendant induced retardance) in opticalelements used in high precision instruments employed in semiconductorand other industries. The optics industry thus has a need for a highlysensitive instrument for measuring linear birefringence in opticalcomponents. This need has been largely unmet, especially with respect tomeasurements of low levels of retardance.

[0005] Linearly polarized light may also be characterized as thesuperposition of two components of circularly polarized light(right-hand and left-hand senses) having identical amplitude andfrequency or wavelength. The relative phases of the two circularpolarization components determines the polarization plane. The plane ofpolarization will be rotated in instances where the refractive indicesof a sample are slightly different for the two senses of circularpolarization. This rotation of the polarization plane is referred to asoptical rotation. Optical rotation is also referred to as circularbirefringence because it relates to the phase shifting of the circularpolarization components that is attributable to the different refractiveindices.

[0006] If linearly polarized light passes through chiral media, such as,for example a solution of chiral molecules, the polarization of theincident light will be rotated. This circular birefringence (or opticalrotation) is often referred to as natural optical rotation todistinguish it from Faraday rotation in a magnetic field. The extent ofoptical rotation, therefore, is indicative of the molecular structure(the chirality) of such media. Thus, the precise detection and analysisof the optical rotation, or circular birefringence, imparted by sampleof chiral medial is useful for analytical chemistry, pharmaceutical, andbiological industries.

[0007] The complete description of each linear and circularbirefringence requires two parameters. Both linear and circularbirefringence of a sample along a given optical path require specifyingthe magnitude of the birefringence, or the amount of integrated phaseretardation along the given optical path length. For linearbirefringence, it is also required to specify the fast axis of thesample. The two orthogonal polarization components described above areparallel to two orthogonal axes, which are determined by the sample andare called the “fast axis” and the “slow axis.” The fast axis is theaxis of the material that aligns with the faster moving component of thepolarized light through the sample. For circular birefringence, thesense of optical rotation, in terms of clockwise or anticlockwise,should be specified. Therefore, a complete description of the linear andcircular birefringence of a sample along a given optical path requiresspecifying both the magnitude of the birefringence, the relative angularorientation of the fast (or slow) axis, and the rotational direction(for circular birefringence).

[0008] The present invention is directed to a practical system andmethod for precisely measuring low-level linear and circularbirefringence properties of optical materials. The retardance magnitudeand orientation of the fast axis are precisely calculated, as well asthe rotational direction. The system permits multiple measurements to betaken across the area of a sample to detect and graphically displayvariations in the retardance across the sample area.

[0009] In a preferred embodiment, the system incorporates a photoelasticmodulator for modulating polarized light that is then directed through asample. The beam propagating from the sample is separated into twoparts. These separate beam parts are then analyzed at differentpolarization directions, detected, and processed as distinct channels.The detection mechanisms associated with each channel detect the lightintensity corresponding to each of the two parts of the beam. Thisinformation is employed in an algorithm for calculating a precise,unambiguous measure of the retardance induced by the sample and theorientation of the fast axis.

[0010] As one aspect of this invention, the system includes abeam-splitting member and detector arrangement that permits splittingthe beam into two parts with minimal contribution to the retardanceinduced in the beam. Moreover, the presence of any residualbirefringence in the optical system (such as may reside as staticbirefringence in the photoelastic modulator or in any of the opticalcomponents of the system) is accounted for in a number of ways. Forexample, certain of the system components are arranged or mounted tominimize the chance that strain-induced birefringence may be impartedinto the element. A reliable calibration technique is also provided.

[0011] The system permits the low-level linear and circularbirefringence measurements to be taken at any of a plurality oflocations across the area of the sample. The measurements are compiledin a data file and graphically displayed for quick analysis.

[0012] In one embodiment of the invention, the optical components of thesystem are arranged to measure the birefringence properties of a samplethat is reflectively coated on one side, thereby permitting measurementof birefringence properties even though the sample is not completelylight transmissive.

[0013] Other advantages and features of the present invention willbecome clear upon study of the following portion of this specificationand drawings.

BRIEF DESCRIPTION OF DRAWINGS

[0014]FIG. 1 is a diagram of a preferred embodiment of the presentsystem showing the preferred arrangement of the optical components.

[0015]FIG. 2 is a block diagram of the processing components of thepresent system illustrating the processing of linear birefringence.

[0016]FIG. 3 is a perspective view of detection and beam-splittingcomponents of the system.

[0017]FIG. 4 is a cross-sectional view of one of the detector assembliesof the system.

[0018]FIG. 5 is a perspective view of the primary components of aphotoelastic modulator that is incorporated in the present system.

[0019]FIG. 6 is a drawing depicting a graphical display provided by thesystem of the present invention.

[0020]FIG. 7 is a diagram of an alternative embodiment of the presentinvention.

[0021]FIG. 8 is a graph that plots, for a selected retardance, theoscillation amplitude of the polarization modulator against a number ofsource-light wavelengths, for a polarization modulator that employs apreferred type of optical element.

[0022]FIG. 9 is a graph, based in part on the data shown in FIG. 8, thatrepresents a correction factor that may be applied to convert theretardance value of an optical-material sample as measured at onesource-light wavelength to the retardance value that would occur in thesample at another source-light wavelength.

[0023]FIG. 10 is a graph that plots, for a selected retardance, theoscillation amplitude of the polarization modulator against a number ofsource-light wavelengths, for a polarization modulator that employs analternative type of optical element.

[0024]FIG. 11 is a another graph, like FIG. 9, that represents acorrection factor that may be applied to convert the retardance value ofan optical-material sample as measured at one source-light wavelength tothe retardance value that would occur in the sample at anothersource-light wavelength.

[0025]FIG. 12 is a block diagram of the processing components of thepresent system illustrating the processing of circular birefringence.

BEST MODES FOR CARRYING OUT THE INVENTION

[0026] Linear Retardance Measurement

[0027] The diagram of FIG. 1 depicts the primary optical components of asystem made in accordance with the present invention. The componentsinclude a HeNe laser as a light source 20 that has a wavelength of 632.8nanometers (nm). The beam “B” emanating from the source has a crosssectional area or “spot size” of approximately 1 millimeter (mm).

[0028] The source light beam “B” is directed to be incident on apolarizer 22 that is oriented with its polarization direction at +45°relative to a baseline axis. A high-extinction polarizer, such as aGlan-Thompson calcite polarizer, is preferred. It is also preferred thatthe polarizer 22 be secured in a precision, graduated rotator.

[0029] The polarized light from the polarizer 22 is incident on theoptical element 25 of a photoelastic modulator 24 (FIGS. 1 and 5). In apreferred embodiment, the photoelastic modulator (hereafter referred toas a “PEM”) is one manufactured by Hinds Instruments, Inc., ofHillsboro, Oreg., as a low birefringence version of Model PEM-90 I/FS50.It is noteworthy here that although a PEM is preferred, one couldsubstitute other mechanisms for modulating the polarization of thesource light.

[0030] The PEM has its birefringent axis oriented at 0° and iscontrolled by a controller 84 that imparts an oscillating birefringenceto the optical element 25, preferably at a nominal frequency of 50 kHz.In this regard, the controller 84 drives two quartz transducers 29between which the optical element 25 is bonded with an adhesive.

[0031] The oscillating birefringence of the PEM introduces atime-varying phase difference between the orthogonal components of thepolarized light that propagates through the PEM. At any instant in time,the phase difference is the retardation introduced by the PEM. Theretardation is measurable in units of length, such as nanometers. ThePEM is adjustable to allow one to vary the amplitude of the retardationintroduced by the PEM. In the case at hand, the retardation amplitude isselected to be 0.383 waves (2.405 radians).

[0032] The beam of light propagating from the PEM is directed throughthe transparent sample 26. The sample is supported in the path of thebeam by a sample stage 28 that is controllable for moving the sample ina translational sense along orthogonal (X and Y) axes. The stage may beany one of a number of conventional designs such as manufactured by THKCo. Ltd., of Tokyo, Japan as model KR2602 A-250. As will become clear,the motion controllers of the sample stage 28 are driven to enablescanning the sample 26 with the beam to arrive at a plurality ofretardance and orientation measurements across the area of the sample.

[0033] The sample 26 will induce retardance into the beam that passesthrough it. It is this retardance value that is determined in accordancewith the processing provided by the present invention, as explained morebelow. The present system is especially adapted to determine low levelsof retardance. Low retardance levels are determined with a sensitivityof less than ±0.01 nm.

[0034] In order to obtain an unambiguous measure of the sample-inducedretardance, the beam “Bi” that passes out of the sample is separatedinto two parts having different polarization directions and therebydefining two channels of information for subsequent processing.

[0035] Turning first to the preferred mechanism for separating the beam“Bi,” there is located in the path of that beam (hereafter referred toas the incidence path) a beam-splitting mirror 30. Part “B1” of the beam“Bi” passes completely through the beam-splitting mirror 30 and enters adetector assembly 32 for detection.

[0036]FIG. 3 depicts a preferred mechanism for supporting thebeam-splitting mirror 30. In particular, the mirror 30 is seated in thecentral aperture of a housing 31 that is rigidly supported by an arm 33to a stationary vertical post 36. The post 36 is employed for supportingall of the optical components of the system so that the paths of thelight are generally vertical.

[0037] The diameter of the mirror 30 is slightly less than the diameterof the housing aperture. The aperture is threaded except for an annularshoulder that projects into the lowermost end of the aperture to supportthe periphery of the flat, round mirror 30. A retainer ring 40 isthreaded into the aperture to keep the mirror in place in the housing 31against the shoulder.

[0038] In a preferred embodiment, care is taken to select and mount themirror 30 so that substantially no stress-induced birefringence isintroduced into the mirror. In this regard, the mirror is preferablymade of Schott Glass type SF-57 glass. This glass has an extremely low(near zero) stress-optic coefficient. The retainer ring 40 is carefullyplaced to secure the mirror without stressing the glass. Alternatively,flexible adhesive may be employed to fasten the mirror. No setscrews orother stress-inducing mechanisms are employed in mounting the mirror.

[0039] It is noteworthy here that, although a beam-splitting mirror ispreferred, one can substitute other mechanisms (such as a flipper mirrorarrangement) for separating the beam “Bi” into two parts.

[0040] The part of the beam “B1” that passes through the mirror 30enters the detector assembly 32 (FIG. 1), which includes a compact,Glan-Taylor type analyzer 42 that is arranged such that its polarizationdirection is at −45° from the baseline axis. From the analyzer 42, thebeam “B1” enters a detector 44, the particulars of which are describedmore below.

[0041] The reflective surface 35 of the beam-splitting mirror 30 (FIG.3) faces upwardly, toward the sample 26. The mirror is mounted so thatthe incidence path (that is, the optical path of the beam “Bi”propagating from the sample 26) is nearly normal to the reflectivesurface 35. This orientation is preferred for substantially eliminatingretardance that would otherwise be introduced by an optical componentthat is called on to redirect the path of the beam by more than a fewdegrees.

[0042]FIG. 1 shows as “A” the angle made between the beam “Bi” travelingalong the incidence path and the beam part “Br” that is reflected fromthe mirror 30. Angle “A” is shown greatly enlarged for illustrativepurposes. In a preferred embodiment, this angle is greater than 0° butless than 10°. Most preferred is an angle “A” of under 5°.

[0043] The reflected part of the Beam “Br” is incident upon anotherdetector assembly 50. That assembly 50 is mounted to the post 36 (FIG.3) and configured in a way that permits the assembly to be adjacent tothe incident beam “Bi” and located to receive the reflected beam “Br.”More particularly, the assembly 50 includes a base plate 52 that is heldto the post 36 by an any 54. As seen best in FIG. 4, the base plateincludes an inner ring 57 that is rotatably mounted to the base plateand has a large central aperture 56 that is countersunk to define in thebottom of the plate 52 an annular shoulder 58.

[0044] The detector components are compactly integrated and contained ina housing 60 that has a flat front side 62. The remainder of the side ofthe housing is curved to conform to the curvature of the centralaperture 56 of the base plate 52. Moreover, this portion of the housing60 includes a stepped part 64 that permits the curved side of thehousing to fit against the base plate 52 and be immovably fastenedthereto.

[0045] A sub-housing 70 is fastened inside of the detector componentshousing 60 against the flat side 62. The sub-housing 70 is a generallycylindrical member having an aperture 72 formed in the bottom. Justabove the aperture 72 resides a compact, Glan-Taylor type analyzer 74that is arranged so that its polarization direction is 0°, parallel withthat of the PEM 24.

[0046] Stacked above the analyzer 74 is a narrow-band interferencefilter 77 that permits passage of the polarized laser light but blocksunwanted room light from reaching a detector 76. The detector ispreferably a photodiode that is stacked above the filter. The photodiodedetector 76 is the preferred detection mechanism and produces as outputa current signal representative of the time varying intensity of thereceived laser light. With respect to this assembly 50, the laser lightis that of the beam “B2,” which is the reflected part “Br” of the beamthat propagated through the sample 26.

[0047] The photodiode output is delivered to a preamplifier carried onan associated printed circuit board 78 that is mounted in the housing60. The preamplifier 75 (FIG. 2) provides output to a phase sensitivedevice (preferably a lock-in amplifier 80) in the form of alow-impedance intensity signal V_(AC), and a DC intensity signal V_(DC),which represents the time average of the detector signal.

[0048] It is noteworthy here that the other detector assembly 32 (FIG.3) to which is directed the non-reflected part “B1” of the beam “Bi” is,except in two respects, the same construction as the just describedassembly 50. As shown in FIG. 3, the detector assembly 32 is mounted tothe post 36 in an orientation that is generally inverted relative tothat of the other detector assembly 50. Moreover, the analyzer 42 ofthat assembly 32 is arranged so that its polarization direction isoblique to the polarization direction of the analyzer 74 in the otherdetector assembly 50. Specifically, the analyzer 42 is positioned withits polarization direction at −45°. The preferred analyzer position isestablished by rotating the detector assembly via the inner ring 57discussed above.

[0049] The photodiode of detector assembly 32 produces as output acurrent signal representative of the time varying intensity of thereceived laser light. With respect to this assembly 32, the laser lightis that of the beam “B1,” which is the non-reflected part of the beam“Bi” that propagated through the sample 26.

[0050] The photodiode output of the detector assembly 32 is delivered toa preamplifier 79, which provides its output to the lock-in amplifier 80(FIG. 2) in the form of a low-impedance intensity signal V_(AC), and aDC intensity signal V_(DC), which represents the time average of thedetector signal.

[0051] In summary, the lock-in amplifier 80 is provided with twochannels of input: channel 1 corresponding to the output of detectorassembly 32, and channel 2 corresponding to the output of detectorassembly 50. The intensity information received by the lock-in amplifieron channel I—because of the arrangement of the −45° analyzer 42—relatesto the 0° or 90° component of the retardance induced by the sample 26.The intensity information received on channel 2 of the lock-in amplifier80—as a result of the arrangement of the 0° analyzer 74—relates to the45° or −45° component of the retardance induced by the sample. Asexplained below, this information is combined in an algorithm thatyields an unambiguous determination of the magnitude of the overallretardance induced in the sample (or a location on the sample) as wellas the orientation of the fast axis of the sample (or a location on thesample).

[0052] The lock-in amplifier 80 may be one such as manufactured by EG&GInc., of Wellesley, Mass., as model number 7265. The lock-in amplifiertakes as its reference signal 82 the oscillation frequency applied bythe PEM controller 84 to the transducers 29 that drive the opticalelement 25 of the PEM 24. The lock-in amplifier 80 communicates with adigital computer 90 via an RS232 serial interface.

[0053] For a particular retardance measurement, such as one taken duringthe scanning of several locations on a sample, the computer 90 obtainsthe values of channel 1. The computer next obtains the values of channel2. The intensity signals on the detectors in channels 1 and 2 arederived as follows: $\begin{matrix}\begin{matrix}{I_{ch1} = {1 + {{\cos \left( {4\quad \rho} \right)}{\sin^{2}\left\lbrack \frac{\delta}{2} \right\rbrack}\cos \quad \Delta} - {{\cos^{2}\left\lbrack \frac{\delta}{2} \right\rbrack}\cos \quad \Delta} + {{\cos \left( {2\quad \rho} \right)}\sin \quad \delta \quad \sin \quad \Delta}}} \\{I_{ch2} = {1 + {{\sin \left( {4\quad \rho} \right)}{\sin^{2}\left\lbrack \frac{\delta}{2} \right\rbrack}\cos \quad \Delta} + {{\sin \left( {2\quad \rho} \right)}\sin \quad \delta \quad \sin \quad \Delta}}}\end{matrix} & {{Eqn}.\quad (1)}\end{matrix}$

[0054] where Δ is the PEM's time varying phase retardation; δ is themagnitude of the sample's retardance; and ρ is the azimuth of the fastaxis of the sample's retardance.

[0055] The Mueller matrix for a linearly birefringent sample (δ, ρ) usedin the derivation has the following form: $\begin{bmatrix}1 & 0 & 0 & 0 \\0 & {{{\cos \left( {4 \cdot \rho} \right)} \cdot {\sin \left( \frac{\delta}{2} \right)}^{2}} + {\cos \left( \frac{\delta}{2} \right)}^{2}} & {{\sin \left( {4 \cdot \rho} \right)} \cdot {\sin \left( \frac{\delta}{2} \right)}^{2}} & {{- {\sin \left( {2 \cdot \rho} \right)}} \cdot {\sin (\delta)}} \\0 & {{\sin \left( {4 \cdot \rho} \right)} \cdot {\sin \left( \frac{\delta}{2} \right)}^{2}} & {{- \left( {{\cos \left( {4 \cdot \rho} \right)} \cdot {\sin \left( \frac{\delta}{2} \right)}^{2}} \right)} + {\cos \left( \frac{\delta}{2} \right)}^{2}} & {{\cos \left( {2 \cdot \rho} \right)} \cdot {\sin (\delta)}} \\0 & {{\sin \left( {2 \cdot \rho} \right)} \cdot {\sin (\delta)}} & {- \left( {{\cos \left( {2 \cdot \rho} \right)} \cdot {\sin (\delta)}} \right)} & {\cos (\delta)}\end{bmatrix}\quad$

[0056] In equations (1), sin Δ (Δ=Δ0 sin ωt, where ω is the PEM'smodulating frequency; Δ₀ is the maximum peak retardance of the PEM) canbe expanded with the Bessel functions of the first kind: $\begin{matrix}{{\sin \quad \Delta} = {{\sin\left( {\Delta_{0}{\sin \left( {\omega \quad t} \right)}} \right)} = {\sum\limits_{{2k} + 1}{2\quad {J_{{2k} + 1}\left( \Delta_{0} \right)}{\sin\left( {\left( {{2k} + 1} \right){\omega t}} \right)}}}}} & {{Eqn}.\quad (2)}\end{matrix}$

[0057] where k is either “0” or a positive integer; and J_(2k+1) is the(2k+1)th order of the Bessel function. Similarly, cos Δ can be expandedwith the even harmonics of the Bessel functions: $\begin{matrix}\begin{matrix}{{\cos \quad \Delta} = {\cos \left( {\Delta_{0}{\sin \left( {\omega \quad t} \right)}} \right)}} \\{= {{J_{0}\left( \Delta_{0} \right)} + {\sum\limits_{2k}{2{J_{2k}\left( \Delta_{0} \right)}{\cos \left( {\left( {2k} \right)\omega \quad t} \right)}}}}}\end{matrix} & {{Eqn}.\quad (3)}\end{matrix}$

[0058] where J₀ is the 0^(th) order of the Bessel function, and J_(2k)is the (2k)th order of the Bessel function.

[0059] As seen from equations 1-3, it is preferable to determine themagnitude and angular orientation of retardance using the signal at thePEM's first harmonic. The useful signal for measuring linearbirefringence at the PEM's 2nd harmonic is modified by sin²(δ/2), avalue that is much smaller than sin δ. The 1F electronic signal on thedetectors can be expressed in equation (4):

I _(ch 1,1F)=sin δ cos(2ρ)2J ₁(Δ₀)sin(ωt)

I _(ch 2,1F)=sin(2ρ)2J ₁(Δ₀)sin(ωt)  Eqn. (4)

[0060] As noted, the 1F signal is determined using the lock-in amplifier80 that is referenced at the PEM's first harmonic. The lock-in amplifierwill exclude the contributions from all harmonics other than 1F. Theoutput from the lock-in amplifier 80 for the two channels is:$\begin{matrix}\begin{matrix}{{{I_{ch1}\left( {1F} \right)}\sqrt{2}} = {\frac{I_{0}}{2}\quad \delta \quad {\cos \left( {2\quad \rho} \right)}2\quad {J_{1}\left( \Delta_{0} \right)}}} \\{{{I_{ch2}\left( {1F} \right)}\sqrt{2}} = {\frac{I_{0}}{2}\quad \delta \quad {\sin \left( {2\quad \rho} \right)}2\quad {J_{1}\left( \Delta_{0} \right)}}}\end{matrix} & {{Eqn}.\quad (5)}\end{matrix}$

[0061] Using the approximation of sin δ≈δ for low-level linearbirefringence; and {square root}2 results from the fact that the lock-inamplifier measures the r.m.s. of the signal, instead of the amplitude.

[0062] All terms appearing at a frequency other than the PEM's firstharmonic are neglected in obtaining equations (5). The validity ofequations (5) for obtaining the 1F V_(AC) signal is further ensured fromthe approximation that sin²(δ/2)≈0 when δ is small. This applies forlow-level retardance of, for example, less than 20 nm.

[0063] In order to eliminate the effect for intensity fluctuation of thelight source, or variations in transmission due to absorption,reflection losses, or scattering, the ratio of the 1F VAC signal to theVDC signal is used. (Alternatively, similar techniques can be employed,such as dynamically normalizing the DC signal to unity.) Exclusion ofthe cos Δ terms in equation (1) can severely affect the VDC signal inchannel I even though it has a minimal effect on the determination ofthe 1F VAC signal using a high quality lock-in amplifier. The DC term ofchannel I depends on J₀(Δ₀) as seen from equation (6). $\begin{matrix}{\begin{matrix}{I_{d\quad {c1}} = {\frac{I_{0}}{2}\left( {1 - {J_{0}\left( \Delta_{0} \right)}} \right)}} \\{I_{d\quad {c2}} = \frac{I_{0}}{2}}\end{matrix}\quad.} & {{Eqn}.\quad (6)}\end{matrix}$

[0064] Consequently, this DC term should be corrected as in equation(7): $\begin{matrix}\begin{matrix}{{\frac{I_{ch1}\left( {1F} \right)}{I_{d\quad {c1}}} \cdot \frac{1 - {J_{0}\left( \Delta_{0} \right)}}{2\quad {J_{1}\left( \Delta_{0} \right)}} \cdot \sqrt{2}} = {R_{ch1} = {\delta \quad {\cos \left( {2\quad \rho} \right)}}}} \\{{\frac{I_{ch2}\left( {1F} \right)}{I_{d\quad {c2}}} \cdot \frac{1}{2\quad {J_{1}\left( \Delta_{0} \right)}} \cdot \sqrt{2}} = {R_{ch2} = {\delta \quad {\sin \left( {2\quad \rho} \right)}}}}\end{matrix} & {{Eqn}.\quad (7)}\end{matrix}$

[0065] where R_(ch1) and R_(ch2) are experimentally determinedquantities from the two channels.

[0066] To correct the “DC” term caused by the cos Δ term in channel I,one properly sets the PEM retardation so that J₀(Δ₀)=0 (when Δ₀=2.405radians, or 0.383 waves). At this PEM setting, the efficiency of the PEMfor generating the 1F signal is about 90% of its maximum.

[0067] Finally, the magnitude and angular orientation of the linearbirefringence is expressed in equations (8): $\begin{matrix}\begin{matrix}{\rho = {\frac{1}{2}{\tan^{- 1}\left\lbrack \frac{R_{ch2}}{R_{ch1}} \right\rbrack}}} & {or} & {\rho = {\frac{1}{2}{{ctg}^{- 1}\left\lbrack \frac{R_{ch1}}{R_{ch2}} \right\rbrack}}} \\{\delta = \sqrt{\left( R_{ch1} \right)^{2} + \left( R_{ch2} \right)^{2}}} & \quad & \quad\end{matrix} & {{Eqn}.\quad (8)}\end{matrix}$

[0068] These equations (8) are compiled in a program running on thecomputer 90 and used to determine the magnitude and orientation of theretardance at any selected point on the sample.

[0069] Equations (8) are specifically developed for small linearbirefringence. The approximation of sin δ≈δ used in deriving equations(8) has an error of ˜1% for δ=20 nm when the light wavelength is at632.8 nm. For any larger retardation, sin δ should be used, instead ofδ.

[0070] As noted above, best retardance measurement results are achievedwhen one minimizes the residual birefringence present in the opticalcomponents of the system. To this end, the present system employs a PEM24 (FIG. 5) that is specially configured to eliminate residualbirefringence that may be attributable to supporting the optical element25 of the PEM in the housing 27 (shown in dashed lines of FIG. 5). Thebar-shaped optical element is bonded at each end to a transducer 29.Each transducer 29 is mounted to the PEM housing 27, as by Supports 23,so that the optical element is essentially suspended, thus free (rollany residual birefringence that may be attributable to directly mountingthe oscillating optical element 25 to the PEM housing 27.

[0071] Notwithstanding efforts such as the foregoing to eliminateresidual birefringence in the system components, the presence of atleast some level of residual birefringence is inevitable. In the presentsystem, highly accurate results are obtained by correcting the resultsof equations 8 to account for any remaining residual birefringence inthe system, which residual may be referred to as the system offset. Inpractice, residual birefringence in the optical element of thephotoelastic modulator and in the beam-splitting mirror substrate caninduce errors in the resulting measurements. Any such errors can bemeasured by first operating the system with no sample in place. Acorrection for the errors is made by subtracting the error values foreach channel.

[0072] The system offset is obtained by making a measurement without asample in place. The results from both channels 1 and 2 are the systemoffsets at 0° and 45° respectively: $\begin{matrix}\begin{matrix}{R_{ch1}^{0} = {\frac{I_{ch1}^{0}\left( {1F} \right)}{2\quad {J_{1}\left( \Delta_{0} \right)}I_{d\quad {c1}}^{0}} = {\delta^{0}\quad \left( {\rho = 0} \right)}}} \\{R_{ch2}^{0} = {\frac{I_{ch2}^{0}\left( {1F} \right)}{2\quad {J_{1}\left( \Delta_{0} \right)}I_{d\quad {c2}}^{0}} = {\delta^{0}\quad \left( {\rho = \frac{\pi}{4}} \right)}}}\end{matrix} & {{Eqn}.\quad (9)}\end{matrix}$

[0073] where the superscript “0” indicates the absence of a sample. Theequation bearing the term ρ=0 corresponds to channel 1 (the −45°analyzer 42). The equation bearing the term ρ=π/4 corresponds to channel2 (the 0° analyzer 74). The system offsets are corrected for bothchannels when a sample is measured. The system offsets for channels 1and 2 are constants (within the measurement error) at a fixedinstrumental configuration. Barring any changes in the components of thesystem, or in ambient pressure or temperature, the system should remaincalibrated.

[0074] In principle, this procedure will provide a method ofself-calibration of the system. It is, however, prudent to compare thesystem measurement of a sample with the measurement obtained using othermethods.

[0075] One such calibration sample may be provided by a compoundzero-order waveplate. The compound waveplate comprises twomultiple-order waveplates (e.g., quartz) or two zero-order waveplates(e.g., mica) selected to have a very small retardance difference betweenthem (e.g., less than 0.03 wavelengths). They would be combined withtheir axes at right angles so that the retardance of one is subtractedfrom the other to produce the sought-after low-level retardance,compound zero-order waveplate(s) for use in calibration. Such aconfiguration will provide a uniform retardance across the surface witha low temperature coefficient of retardance.

[0076] If the components of the present system are correctly set up, themagnitude of the measured, sample-induced retardance will be independentof the sample's angular orientation. This angular independence may belost if: (1) the polarization directions of the polarizer 22 andanalyzers 42, 74 are not precisely established, and (2) the maximum peakretardance of the PEM is not precisely calibrated. What follows is adescription of correction techniques for eliminating the just mentionedtwo sources of possible “angular dependence” errors.

[0077] As respects the precise establishment of the polarizationdirections of the polarizer 22 and analyzers 42, 74, the correctiontechnique applied to the polarizer 22 involves the following steps:

[0078] 1. With the PEM operating, approximately orient the polarizer 22and the channel 1 analyzer/detector assembly 32 at 45° and 45′,respectively.

[0079] 2. Rotate the polarizer 22 in fine increments while monitoringthe 2F (100 kHz) lock-in amplifier signal from channel 1. When the 2Fsignal reaches “0” (practically, the noise level at the highest lock-inamplifier sensitivity possible), read precisely the angle on thepolarizer rotator.

[0080] 3. Rotate the polarizer 22 by precisely 45°, which is the correctposition for the polarizer.

[0081] 4. Once the position of the polarizer 22 is correctlyestablished, turn off the PEM and rotate analyzer/detector assembly 32while monitoring the lock-in amplifier's V_(DC) signal from channel 1.When the minimum V_(DC) signal is achieved, the position ofanalyzer/detector assembly 32 is set correctly.

[0082] 5. Once the position of the polarizer 22 is correctlyestablished, rotate analyzer/detector assembly 50 while monitoring thelock-in amplifier's 2F (100 kHz) signal from channel 2. When this 2Fsignal reaches “0” (practically, the noise level at the highest lock-inamplifier sensitivity possible), the position of analyzer/detectorassembly 50 is set correctly.

[0083] As respects the calibration of the PEM, the following techniquemay be employed:

[0084] 1. Set the channel 1 analyzer/detector assembly 32 at −45° whenthe polarizer 22 is at +45°.

[0085] 2. Record the V_(DC) signals with a precision voltmeter while thePEM retardance is changed in the vicinity of, for example, ±10% of theselected peak retardance of the PEM.

[0086] 3. Set the channel 1 analyzer/detector assembly 32 at +45°.

[0087] 4. Record V_(DC) signals with a precision voltmeter while the PEMretardance is changed in the selected vicinity.

[0088] 5. Plot the two V_(DC) curves against PEM retardation around theselected peak retardance. The intersection of the two curves is theretardance for J₀=0.

[0089] 6. Set the PEM retardance value at the intersection value of step5.

[0090] As mentioned above, the motion controllers of the sample stage 28are controlled in a conventional manner to incrementally move the sample26 about orthogonal (X, Y) axes, thereby to facilitate a plurality ofmeasurements across the area of a sample. The spatial resolution ofthese measurements can be established as desired (e.g., 3.0 mm),provided that the sought-after resolution is not finer than the crosssection of the beam that strikes the sample. In this regard, the crosssectional area or “spot size” of the laser beam may be minimized, ifnecessary, by the precise placement of a convex lens with an appropriatefocal length, such as shown as line 96 in FIG. 1, between the lightsource 20 and the polarizer 22. The lens could be, for example,removably mounted to the top of the polarizer 22. The lens 96 would bein place in instances where a very small spot size of, for example, 0.1mm (and corresponding spatial resolution) is desired for a particularsample.

[0091] In some instances it may be desirable to enlarge the spot sizeprovided by the laser source. To this end a lens or lens system such asprovided by a conventional beam expander may be introduced into thesystem between the laser 20 and the polarizer 22.

[0092] The measured retardance values can be handled in a number ofways. In a preferred embodiment the data collected from the multiplescans of a sample are stored in a data file and displayed as a plot on acomputer display 92. One such plot 100 is shown in FIG. 6. Each cell 102in a grid of cells in the plot indicates a discrete location on thesample. The magnitude of the retardance is depicted by color coding.Here different shadings in the cells represent different colors. In FIG.6, only a few different colors and cells are displayed for clarity. Itwill be appreciated, however, that a multitude of cells can bedisplayed. The legend 104 on the display correlates the colors (thecolor shading is omitted from the legend) to a selectable range ofretardance values within which the particular measurement associatedwith a cell 102 falls. A line 106 located in each cell 102 extendsacross the center of each cell and presents an unambiguous visualindication of the full physical range (−90° to +90°) of the orientationof the fast axis of the sample at each sampled location. Thus, theorientation of the fast axis and the retardance magnitude measurementsare simultaneously, graphically displayed for each location. With such acomplete, graphical display, an inexperienced operator user is lesslikely to make errors in analyzing the data that are presented.

[0093] In a preferred embodiment, the just described retardancemeasurements are displayed for each cell as soon as that cell'sinformation is computed. As a result of this instantaneous displayapproach, the operator observes the retardance value of each cell,without the need to wait until the retardance values of all of the cellsin the sample have been calculated. This is advantageous for maximizingthroughput in instances where, for example, an operator is charged withrejecting a sample if the birefringence value of any part of the sampleexceeds an established threshold.

[0094] Also illustrated in FIG. 6 is a contour line placed there as anexample of a contour line that follows a common measured range ofretardation magnitude. For simplicity, only a single one of severalcontour lines is shown for the low-resolution plot of FIG. 6.

[0095] It will be appreciated that any of a number of variations fordisplaying the measured data will suffice. It will also be apparent fromFIG. 6 that the means for setting parameters of how the sample isscanned (scan boundaries, grid spacing sample thickness, etc.) and theresulting data are conveniently, interactively displayed.

[0096] Another approach to graphically displaying the retardancemagnitude and orientation information provided by the present system isto depict the retardance magnitude for a plurality of locations in asample via corresponding areas on a three-dimensional contour map. Theassociated orientations are simultaneously shown as lines or colors incorresponding cells in a planar projection of the three dimensional map.

[0097]FIG. 7 depicts an arrangement for measuring retardance magnitudeand orientation in a sample 124 that is reflectively coated on one side.Apart from the different sample 124 and the relative locations of theoptical components, the components of the system of FIG. 7 match thoseof the embodiment of FIG. 1 and thus carry the same reference numbers,with a few exceptions as noted below.

[0098] The sample 124 (FIG. 7) is coated on one side with a reflectivesurface, such as very thin layer of chromium. The sample is placed onthe sample stage with the coated surface on the bottom. The beam “B” isdirected to pass through the sample 124. The sample stage is slightlytilted (or, alternatively, the sample is secured in a tilted holdermounted to a flat stage) so that the beam reflects from the coatedsurface toward the beam-splitting mirror 30 and detector assembly 32,which are, in this embodiment, supported above the sample stage 28 asshown. Preferably, these components are located as near as practical tothe beam “B” so that the beam “Bi” reflected from the sample 124 isangled “R” only slightly away (for example 2° to 5°) from the beam “B”propagating from the PEM 24. The beam reflected by the sample (asdistinguished from the beam “Br” reflected by the mirror 30)corresponds, from a processing standpoint, to the beam “Bi” impinging onthe mirror 30 of the FIG. 1 embodiment. Thus, the processing of the twobeam parts “B1” and “B2” are the same for both embodiments. Of course,the measured retardance magnitude of the sample 124 will necessarilycomprise two passes of the beam through the sample. Therefore themeasured value will be divided by two.

[0099] As noted above, it is desirable to locate the beam-splittingmirror 30 as near as practical to the beam “B” so that the beam “Bi”reflected from the sample 124 is angled “R” only slightly away (forexample 2° to 5°) from the beam “B” propagating from the PEM 24. To thisend, the housing 31 may be modified to support a mirror that issemi-circular in shape such that the flat edge of the mirror is locatedadjacent to the beam “B.” The beam “Bi”, therefore, could be reflectedto a location on the mirror that is very close to that edge, hence tothe beam “B” as desired.

[0100] While the present invention has been described in terms ofpreferred embodiments, it will be appreciated by one of ordinary skillin the art that modifications may be made without departing from theteachings and spirit of the foregoing. For example a second lock-inamplifier may be employed (on for each channel) for increasing the speedwith which data is provided to the computer.

[0101] Also, one of ordinary skill will appreciate that sequentialmeasurement using a single detector may be employed for measuring theintensity signal in two different polarization directions and therebydefining two channels of information for subsequent processing. Forexample, a single detector assembly could be employed. This dispenseswith the second detector assembly and the beam-splitter mirror. Such aset-up, however, would require either rotating the analyzer or switchingbetween two polarizers of different orientations to ensure unambiguousretardance measurements and to ascertain the orientation of the fastaxis. Alternatively, the sample and the analyzer may be rotated by 45°.

[0102] The preferred embodiment of the present invention uses a HeNelaser for a stable, pure, monochromatic light source. The HeNe laserproduces a beam having a 632.8 nm wavelength. In some instances,retardance magnitude measurements using light sources having otherfrequencies are desired.

[0103] As another aspect of the present invention, one can develop andapply correction factors to convert the retardance magnitude measurementof the sample as measured by the HeNe laser to the retardance value thatwould occur in the sample at another source-light wavelength. In thisregard, FIG. 8 charts experimental results showing the oscillationamplitude required to produce, via the PEM, a selected peak retardation(such as half-wave) plotted against different source wavelengths for aPEM that employs a fused silica type optical element.

[0104]FIG. 9 is developed by using, in part, the plot of FIG. 8 toproduce a curve that represents a correction factor that is applied tothe retardance magnitude value of the sample as measured at onewavelength (such as the 632.8 nm wavelength of the HeNe laser), therebyto arrive at (either directly or by extrapolation) the retardancemagnitude that would occur in the sample at other wavelengths, such as aUV wavelength of 157 nm. The data in FIG. 9 was generated from anexperiment involving a PEM having a fused silica optical element for usewith samples of similar fused silica material.

[0105] The wavelength correction technique just described for fusedsilica can also be applied to other materials. For example, FIG. 10charts experimental results showing the oscillation amplitude requiredto produce, via the PEM, a selected peak retardation (such as half-wave)plotted against different source wavelengths for a PEM that employs acalcium fluoride optical element.

[0106]FIG. 11 is developed by using the plot of FIG. 10 to produce acurve that represents a correction factor that is applied to theretardance magnitude as measured at one wavelength (such as the 633 nmwavelength of the HeNe laser), thereby to arrive at (either directly orby extrapolation) the retardance magnitude that would occur in thesample at other wavelengths, such as a UV wavelength of 157 nm. The datain FIG. 11 was generated from an experiment involving a PEM having acalcium fluoride optical element for use with samples of similar calciumfluoride material.

[0107] As another approach to correcting the measured retardationmagnitude at one source-light wavelength to relate to the retardationmagnitude at another wavelength, one can refer to the stress-opticcoefficient of the sample material being tested, which coefficient isknown as a function of wavelength. The retardance magnitudes measured attwo different wavelengths are directly proportional to the stress-opticcoefficient of the material.

[0108] Circular Retardance Measurement

[0109] As noted above with respect to FIGS. 1 and 7, the samples 26, 127will induce retardance into the light beam that passes through it. Insome instances the retardance is induced in the beam by a sample (as,for example, chiral media) having circular birefringence. The resultantretardance value (hereafter referred to as (“circular retardance”), inaddition to the value resulting from the linear birefringence discussedabove, is also determined in accordance with the processing provided bythe present invention, as explained more below. The present system isespecially adapted to determine low levels of circular retardance. Lowretardance levels are determined with a sensitivity of about ±1×10⁻⁵radians.

[0110] The determination of the circular retardance employs, in apreferred embodiment, the optical components arrangement shown in thediagram of FIG. 1. This preferred embodiment also employs the sameprocessing components as depicted in FIG. 2, which also appear in FIG.12. FIG. 12 is a modification of the diagram of FIG. 2 for describingthe particular signal processing aspects of this embodiment of theinvention.

[0111] The signal presented by the channel 2 detector assembly 50 (FIG.12) is preferred for determining circular retardance. Using Muellermatrix calculus, signals in channel two can be derived as follows:${\begin{bmatrix}1 & 1 & 0 & 0 \\1 & 1 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix} \cdot \begin{bmatrix}1 & 0 & 0 & 0 \\0 & {\cos \quad \alpha} & {\sin \quad \alpha} & 0 \\0 & {{- \sin}\quad \alpha} & {\cos \quad \alpha} & 0 \\0 & 0 & 0 & 1\end{bmatrix} \cdot \begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & {\cos \quad \Delta} & {\sin \quad \Delta} \\0 & 0 & {{- \sin}\quad \Delta} & \cos\end{bmatrix} \cdot \begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}}->\begin{bmatrix}{1 + {\sin \quad {\alpha \cdot \cos}\quad \Delta}} \\{1 + {\sin \quad {\alpha \cdot \cos}\quad \Delta}} \\0 \\0\end{bmatrix}$

[0112] where Δ is the PEM's time varying phase retardation (Δ=Δ₀ sin ωt,where ω is the PEM's modulating frequency; Δ₀ is the retardationamplitude of the PEM), and a is the magnitude of the circularretardance.

[0113] The light intensity signals at the detector for channel II are:$\begin{matrix}{I_{ch2} = {\frac{I_{0}}{2}\left\{ {1 + {{\sin (\alpha)}\cos \quad \Delta}} \right\}}} & {{{Eqn}.\quad (10)}\quad}\end{matrix}$

[0114] where I₀ is the light intensity after the first polarizer.

[0115] The function of cos Δ in equation 10 can be expanded with theBessel functions of the first kind: $\begin{matrix}{{\cos \quad \Delta} = {{\cos \left( {\Delta_{0}{\sin \left( {\omega \quad t} \right)}} \right)} = {{J_{0}\left( \Delta_{0} \right)} + {\sum\limits_{\quad {2k}}^{\quad}\quad {2{J_{2k}\left( \Delta_{0} \right)}{\cos \left( {\left( {2k} \right)\omega \quad t} \right)}}}}}} & {{Eqn}.\quad (11)}\end{matrix}$

[0116] where J₀ is the 0th order of the Bessel function, and J_(2k) isthe (2k)th order of the Bessel function.

[0117] Substituting equation (11) into equation (10) and taking only upto the second order of the Bessel functions, we obtain: $\begin{matrix}{I_{ch2} = {\frac{I_{0}}{2}\left\{ {1 + {{J_{0}\left( \Delta_{0} \right)}{\sin (\alpha)}} + {2{J_{2}\left( \Delta_{0} \right)}{\sin (\alpha)}{\cos \left( {2\omega \quad t} \right)}} + \ldots} \right\}}} & {{Equ}.\quad (12)}\end{matrix}$

[0118] As seen from equation 12, the detector signal of channel IIcontains “DC” terms, a 2F (cos(2ωt)) term and higher order harmonicterms. It is the 2F “AC” signal that is most useful for determining thecircular birefringence. The 2F “AC” signal can be determined using alock-in amplifier 80 that is referenced at the PEM's second harmonicfrequency. For theoretical evaluation, we assume that a perfect lock-inamplifier will exclude the contributions from all other harmonics. The2F signal measured by the lock-in amplifier for channel II is:$\begin{matrix}{{V_{ch2}\left( {2F} \right)} = {\frac{K_{Ch2}}{\sqrt{2}}\frac{I_{0}}{\sqrt{2}}{\alpha 2}\quad {J_{2}\left( \Delta_{0} \right)}}} & {{Equ}.\quad (13)}\end{matrix}$

[0119] where we have used V_(Ch2)=K_(Ch2)I_(Ch2) (V_(Ch2) is thedetector's electronic signal and K_(Ch2) is an instrumental constant),and the small angle approximations (sin α=α); and {square root}2 resultsfrom the fact that the output of a lock-in amplifier measures theroot-mean-square, not the signal amplitude.

[0120] The “DC” signals for channel II can be derived from equation(12). $\begin{matrix}{{DC}_{ch2} = {\frac{K_{ch2}I_{0}}{2}\left( {1 + {\sin \quad \alpha \quad {J_{0}\left( \Delta_{0} \right)}}} \right)}} & {{Equ}.\quad (14)}\end{matrix}$

[0121] When the PEM retardation amplitude Δ₀=2.405 radians (0.3828waves) is chosen, J₀(Δ₀)=0. At this PEM setting, the 2F signal and the“DC” terms for channel II are: $\begin{matrix}\begin{matrix}{{V_{ch2}\left( {2F} \right)} = {\frac{K_{Ch2}}{\sqrt{2}}\frac{I_{0}}{2}{\alpha 2}\quad {J_{2}\left( \Delta_{0} \right)}}} \\{{DC}_{ch2} = \frac{K_{Ch2}I_{0}}{3}}\end{matrix} & {{Equ}.\quad (15)}\end{matrix}$

[0122] In order to eliminate the effect of light intensity variationsdue to light source fluctuations and the absorption, reflection andscattering from the sample and other optical components, the ratio ofthe 2F “AC” signal to the “DC” signal is used. The ratios of “AC” signalto the “DC” signal for both channels are represented in equation (16):$\begin{matrix}{\frac{V_{ch2}\left( {2F} \right)}{{DC}_{ch2}} = {\sqrt{2}{J_{2}\left( \Delta_{0} \right)}\alpha}} & {{Equ}.\quad (16)}\end{matrix}$

[0123] Finally, the circular birefringence of the sample is expressedas: $\begin{matrix}{\alpha = {\frac{V_{{ch}\quad 2}\left( {2F} \right)}{{DC}_{{ch}\quad 2}} \cdot \frac{1}{\sqrt{2}{J_{2}\left( \Delta_{0} \right)}}}} & {{Equ}.\quad (17)}\end{matrix}$

[0124] here α, represented in radians, is a scalar that can be convertedto degrees.

[0125] The mathematical sign of the α term calculated above isindicative of the direction of rotation of the polarization plane of thebeam. For instance a positive value indicates rotation in the right-handsense; negative meaning rotation in the left-hand sense.

[0126] A single lock-in amplifier 80 (FIG. 12) will suffice for allowingsequential data collection (alternating between channel 1 and channel 2)while the beam B is directed through a single location on the sample. Asa result, the linear retardance value δ and the circular retardance αmay be substantially simultaneously determined for any given sample.

[0127] As indicated in FIG. 12, a group of lock-in amplifiers may beemployed for providing to the computer 90 simultaneously receivedsignals from both channel 1 and channel 2, thereby reducing the overalltime required for simultaneously processing of the linear and circularretardance values for a given location.

[0128] It will be appreciated that the various refinements describedabove with respect to the elimination of residual birefringence in thePEM and system offsets are applicable irrespective of whether linearretardance, circular retardance, or both are determined.

[0129] Similarly, the calibration techniques described above are alsoapplicable when the system is used for calculating circular retardance.Moreover, it is contemplated that, depending on the characteristics ofthe sample, different light source frequencies (that is, other than thepreferred 632.8 nm wavelength HeNe laser) may be desirable.

[0130] It will also be appreciated that the magnitude and rotationdirection of each circular retardance measurement can be stored anddisplayed in a manner as described above with respect to linearretardance magnitude and angle (See FIG. 6). In one preferredembodiment, the display features the simultaneous display (using twowindows) of the detected linear and circular retardance values.

[0131] In some instances it may be desirable to determine the circularretardance of a sample having a reflective coating. Thus, thearrangement of optical components described above with respect to FIG. 7may be employed (allowing, as an option, the simultaneous determinationof the linear retardance of the same sample).

[0132] It is also contemplated that the V₁2F signal transmitted onchannel 1 (FIG. 12) may be measured for a determination of circularretardance. This is not preferred, however, because that signal alsocarries the sample's linear retardance information, which wouldinterfere with the circular retardance information. Also, thedetermination of circular retardance, which depends on cos cc, is muchless accurate when α is small (unless the circular retardance is verylarge).

1. A method of measuring birefringence properties of a sample,comprising the steps of: modulating polarization of light; directing abeam of the modulated light through the sample along an incidence path;reflecting the beam from a reflective surface that is in the incidencepath; analyzing the reflected part of the beam; determining theintensity of the reflected part of the beam; and calculating a circularbirefringence property of the sample based on the determined intensity.2. The method of claim 1 further comprising the steps of; passing afirst part of the beam through the reflective surface; determining theintensity of the first part of the beam; and calculating a linearbirefringence property of the sample based on the determined intensity.3. The method of claim 1 wherein the calculating step includescalculating the magnitude of circular retardance induced by the sample.4. The method of claim 3 wherein the calculating step includescalculating the rotational direction of the circular retardance.
 5. Themethod of claim 2 wherein the analyzing step includes directing thefirst part of the beam through a first analyzer having a firstpolarization direction; and directing the reflected part of the beamthrough a second analyzer having a second polarization direction that isoriented to be different than the polarization direction of the firstanalyzer.
 6. The method of claim 1 including the step of providingoptical system components for carrying out the modulating, directing,reflecting and determining steps; and wherein the calculating stepincludes the step of compensating for residual birefringence present inthe optical components other than the sample.
 7. The method of claim 1wherein the directing step is preceded with the step of passing the beamthrough the sample along a first path and then reflecting the beam backthrough the sample along the incidence path.
 8. The method of claim 1including the steps of: periodically moving the sample so that the beamis directed through a plurality of locations on the sample; andcalculating either or both the circular retardance magnitude of thesample and the rotational direction of the circular retardance of thesample at each location.
 9. The method of claim 2 including the step ofsimultaneously graphically displaying the calculated circularbirefringence property and the calculated linear birefringence property.10. The method of claim 1 wherein the step of determining the intensityof the reflected part of the beam includes supporting an intensitydetector adjacent to the incident path and in the path of the reflectedpart of the beam, thereby to minimize the angle between the incidencepath and the path of the reflected part of the beam.
 11. A method ofmeasuring birefringence properties of a sample, comprising the steps of:modulating polarization of light; directing a beam of the modulatedlight through the sample along an incidence path; dividing the beam intotwo parts; and simultaneously calculating a circular birefringenceproperty of the sample and a linear birefringence property of the samplebased upon the intensities of the divided beam parts.
 12. The method ofclaim 11 including the step of simultaneously displaying the circularbirefringence property of the sample and the linear birefringenceproperty.
 13. The method of claim 1 wherein the calculating stepincludes the step of eliminating the effect of any fluctuation in thebeam intensity.
 14. A system for measuring circular birefringenceproperties in a sample, comprising: a source of light; means forpolarizing the light; modulating means for modulating the polarizationof the light; a sample arranged so that a beam of the modulated lightpasses through the sample along an incidence path; a beam-reflectingelement arranged to reflect along a reflected path a part of the beamthat passes through the sample; an analyzer located in the reflectedpath; and detection means for detecting the intensity of the reflectedpart of the beam, thereby to provide information suitable forcalculating a circular birefringence property of the sample based on thedetected intensity.
 15. The system of claim 14 wherein the means formodulating the polarization of the source light comprises a photoelasticmodulator.
 16. The system of claim 14 wherein the beam directed to thesample has a cross sectional area, the system including a lens memberlocated between the source and the sample for changing the crosssectional area of the beam before the beam moves through the sample. 17.The system of claim 14 wherein the light source is a HeNe laser